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Gabriela Bulancea ([email protected]) Department of Mathematics and Physics, University of Puerto Rico in Cayey, Puerto Rico, On the stability of logmodularity for uniform algebras. ABSTRACT. The main issue in the theory of perturbations of Banach algebras is to determine what properties of a given Banach algebra A are preserved when we slightly deform A by means of deā¦ning a new multiplication between the elements of A, multiplication which is "close" to the original one. We use a characterization theorem for elements of best approximation in normed linear spaces by elements of a linear subspace to address the problem of whether being logmodular is a stable property for uniform algebras. 1